sample_orientation_cone

vector4  sample_orientation_cone(vector4 center, float maxangle, vector u)

center

Orientation in the center of the cone. This does not need to be normalized.

maxangle

Maximum angle, in radians, away from center that any sample of the cone will be, so long as all u values are between 0 and 1.

Note This angle is the maximum quaternion rotation angle between the orientation quaternion that the output represents and center, which is twice the Euclidean cone angle of the unit 4D hypersphere being sampled. A maxangle of π would sample all orientations, but only half of all 4D unit vectors; a maxangle of 2π would sample all 4D unit vectors.

u

Three numbers between 0 and 1.

Returns a unit vector4, i.e. a vector4 of length 1, based on u. Given uniform random u vectors of three values in [0,1), the returned quaternion orientations will be uniform random and continuous with respect to u, in the region of orientations within maxangle of center.